WP descrition: The OLYMPIA project is coordinated by Romain Postoyan (CRAN). Each one of the three technical workpackages is subdivided in two tasks, and is under the responsibility of one coordinator, namely Romain Postoyan (CRAN) for WP1, Sophie Tarbouriech (LAAS) for WP2, and Vincent Andrieu (LAGEPP) for WP3. The interaction and the coordination between the partners will be favoured by the organization of yearly plenary meetings, organized alternatively in Lyon, Nancy and Toulouse, which will bring together the project members. Each meeting will typically last one or two days. One part of the meeting will consist of talks given by project members or external guests presenting their most recent developments in relevant areas for the project. Significant slots will be devoted to presentations given by the students, with the double objective of developing
Coordinator:Romain Postoyan (CRAN)
The OLYMPIA project consists in three technical WorkPackages organized according to the following diagram.
WP descrition: The aim of WP1 is to analyse the robustness properties of nonlinear dynamical systems controlled either by DP algorithms or NN-based feedback laws. In particular, we aim at finding a relevant set of sufficient conditions under which input-to-state stability or Lp stability properties can be ensured. WP1 is naturally structured in two tasks: one dedicated to DP algorithms (Task 1.1), the second to control based on NN (Task 1.2). The outcomes of Tasks 1.1 and 1.2 will then be exploited and merged in WP3.
Coordinators:Romain Postoyan (CRAN)
Participants:Jamal Daafouz (CRAN), Sophie Tarbouriech (LAAS), Vincent Andrieu (LAGEPP), Luca Zaccarian (LAAS), Romain Postoyan (CRAN), Jonathan De Brusse (CRAN), Daniele Astolfi (LAGEPP), Madiha Nadri (LAGEPP), Laurent Bako (LAGEPP).
Task 1.1: Robust stability guarantees for DP-based control
Below is a list of research topics investigated in the context of this Task/WorkPackage
Robust stability with dynamic programming
While dynamic programming algorithms are attractive for their inherent near-optimality guarantees, the question of the robust stability of systems controlled by such algorithms remain largely open. The aim of this task is to contribute to this challenging and important problem.
Task 1.2: Robust stability guarantees for NN controllers
Below is a list of research topics investigated in the context of this Task/WorkPackage
Robust stability with neural networks
Neural networks can be used to construct feedback laws for complex dynamical systems, the question we aim to address is under which conditions such control strategies stabilize the closed-loop system.
Relevant References:
[J2] Simone Mariano, Romain Postoyan, and Luca Zaccarian. Finite-time stability properties of lur’e systems with piecewise continuous nonlinearities. IEEE Transactions on Automatic Control, 2024.
WP descrition: The objectives of WP2 are to modify DP and NN control strategies to endow the closed-loop system with additional desirable properties compared to WP1 (Task 2.1). We also aim at exploiting system theoretic properties to reduce the computation effort associated with these control strategies (Task 2.2).
Coordinators:Sophie Tarbouriech (LAAS)
Participants:Jamal Daafouz (CRAN), Sophie Tarbouriech (LAAS), Vincent Andrieu (LAGEPP), Samuele Zoboli (LAAS), Luca Zaccarian (LAAS), Romain Postoyan (CRAN), Jonathan De Brusse (CRAN), Daniele Astolfi (LAGEPP).
Task 2.1: Redesigning NN and DP algorithms
Below is a list of research topics investigated in the context of this Task/WorkPackage
Tailored dynamic programming algorithms
When a dynamic programming algorithm does not meet desired requirements (like recursive feasibility, robust stabilizing properties etc.), it is needed to redesign or tailor it to suit our purpose. This is the goal of this task.
Task 2.2: Computation-efficient algorithms
Below is a list of research topics investigated in the context of this Task/WorkPackage
WP descrition: The aim of WP3 is to merge the outcomes of WP1 and WP2 to endow systems controlled by N-DP with robust stability and performance guarantees. This workpackage also addresses challenges related to the implementation of such controllers.
Below is a list of research topics investigated in the context of this Task/WorkPackage
Data driven methods
When a model of the plant is not available or too complicated to work with, data-driven methods are an appealing alternative, which are highly compatible with neural networks and dynamic programming algorithms. The challenge in the context of this project is to endow such control strategies with stability guarantees.
Relevant References:
[J1] A. Seuret and S. Tarbouriech. Robust data-driven control design for linear systems subject to input saturation. IEEE Transactions on Automatic Control, 2024.
[P1] A. Iannelli and R. Postoyan. A hybrid systems framework for data-based adaptive control of linear time-varying systems. arXiv preprint arXiv:2405.14426, 2024.
Task 3.2: Finite-iteration algorithms
Below is a list of research topics investigated in the context of this Task/WorkPackage
Safety guarantees
We investigate neuro-dynamic programming control strategies, and more generally optimization-based control methods, to endow the closed-loop systems with safety guarantees (like collision avoidance).
Relevant References:
[J6] R. Ballaben, P. Braun, and L. Zaccarian. Lyapunov-based avoidance controllers with stabilizing feedback. IEEE Control Systems Letters, 2024.
